Ontology, Set Theory, and the Paraphrase Challenge

Journal of Philosophical Logic 50 (6):1231-1248 (2021)
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Abstract

In many ontological debates there is a familiar challenge. Consider a debate over X s. The “small” or anti-X side tries to show that they can paraphrase the pro-X or “big” side’s claims without any loss of expressive power. Typically though, when the big side adds whatever resources the small side used in their paraphrase, the symmetry breaks down. The big side plus small’s resources is a more expressively powerful and thus more theoretically fruitful theory. In this paper, I show that there is a very general solution to this problem, for the small side. Assuming the resources of set theory, small can successfully paraphrase big. This result depends on a theorem about models of set theory with urelements. After proving this theorem, I discuss some of its philosophical ramifications.

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Jared Warren
Stanford University

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References found in this work

Material beings.Peter Van Inwagen - 1990 - Ithaca: Cornell University Press.
Parts of Classes.David K. Lewis - 1991 - Mind 100 (3):394-397.
Material Beings.Peter Van Inwagen - 1990 - Philosophy 67 (259):126-127.

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